2. Ping receives a weekly allowance to purchase soda (x) and juice (y) at school. His preferencesover these two goods can be represented by the utility function U(x,y) =0.5x+ 5lny where xrepresents the number of cans of soda and y represents the number of juice boxes.a) Given his preferences find his Marshallian demand functions for soda (x) and juice (y).b) Suppose that the price of a can of soda is $1.5 and that Ping has $30 to spend on soda andjuice. Write Ping's demand curve for juice (y). Illustrate his demand curve.c) Suppose that the price of a box of juice is $1 (the price of soda and income remain $1.5 and$30, resp.). Use your demand functions to find his best bundle. In an indifference curvediagram illustrate his best bundle at these prices.For the remainder of the question assume that Ping's allowance (income) rises to $36 per week andthe prices of the two goods are unchanged at Px= $1.5 and Py= $1.d) Use your demand functions to find his new best bundle.e) Illustrate the new budget line and the new best bundle that you found above in your diagramfor part (c). Be sure to indicate the slopes of both budget lines.f) What is the income elasticity of soda (as a function of prices and income)?

Given Utility function U=0.5X+5logY where X=Soda Y=Juice Budget constraint M=Px.X+Py.Y

Answered: 2. Ping receives a weekly allowance to…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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10
Q1. Jason has preferences defined over novels (good x) and DVDs (good y) described by the utility function U(x,y)= x2y2. He has income of $120; novels cost $5 each, while DVDs are priced at $15 each. a) Calculate Jason's optimal consumption bundle, AND his maximized utility level Suppose the price of novels increases to $7.5, while the price of DVDs and income are unchanged. b) In the same diagram, draw his old and new budget constraint; AND calculate his nep optimal bundle. c) Calculate the Total Effect (TE), Substitution Effect (SE) and Income Effect (E) of novels associated with the price increase of novels; AND SHOW them in your initial diagram. (Hint: keep 2 decimals if need)
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Suppose an individual is currently spending all of their income on a bundle of books and pizza, but they are not sure whether the bundle maximizes their utility. Assume the individual has a strictly diminishing marginal rate of substitution over these two goods. At their current bundle of books and pizza, the individual's marginal utility from consuming books is 6 utils and their marginal utility from consuming pizza is 3 utils. If the current price of a book is $12 and the price of a pizza is $7, which of the following statements must be true: A. The individual can increase their utility by consuming more books and less pizza B. The individual is maximizing their utility C. The individual can increase their utility by consuming more pizza and fewer books
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Suppose we are able to model the total utility function for the consumption of two goods, good x and good z. The utility function is structured as U(x, z) = 3x2 + z2 - 2xz. The consumer is faced with the prices of goods x and z. The price for each unit of good x and z is $1 each. The consumer has an income $1 (in thousands). How many units of each good should the consumer consume so as to maximize his/her utility?
1) Max chooses to purchase movie tickets and restaurant meals every week with his $100. If the price of a movie ticket is $20 and the price of a restaurant meal is $25, then the slope of his budget constraint will be, a) 1/5 b) -1/5 c) 4/5 d) -4/5 2) Marginal rate of substitution(MRS) is the rate at which consumer is willing to trade one good for another. It must be true that: a) MRS is the slope of an indifference curve in reference to a particular bundle of goods. b) MRS is not the same along an indifference curve that is of usual shape. c) MRS is same along an indifference curve that is of usual shape. d) Both a) and b).
1 FOOD STAMPS Consider a person who has $750 per month in income and has preferences for food (F) and all other goods (X) represented by a utility function, U(F, X) = F⁰.2 X0.8. To simplify analysis, let's assume that both the price of food and the price of all other goods is $1 per unit such that F and X represent expenditure on food and all other goods, respectively. a. Set up a Lagrangian and derive the consumer's demand functions for food and all other goods. As you are solving, make sure you can explain each step in words. b. Now solve for the demand functions using the "substitution approach" whereby we sub- stitute the constraint directly into the objective function. Show that the resulting demand functions are the same as in part (a). c. What is the consumer's optimal bundle given the prices and income? How much utility does the consumer derive from this bundle? Now assume that the government introduces a Food Stamps program that gives this con- sumer $250 that she can only…
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Suppose that U(f,c) = f + 8c^(1/2)is a utility function that describes Amelia’s preferences over two goods: fish(f)and custard (c). For the following, think of fish as the good graphed on the horizontal axis.a. Derive an expression for her marginal utility (Uf)from a small increase in f holding c fixed. Also find themarginal utility for custard (Uc).b. What is Amelia’s marginal rate of substitution (MRS)? Give a brief (2 sentences maximum) intuitivedescription of what MRS represents. If Amelia has 4 units of custard, holding her utility constant, howmany units of custard would she be willing to give up in order to get one more unit of fish?c. Graph Amelia’s indifference curve for a utility level of 40. Be sure to specify at least 3 bundles of goodson the indifference curve.d. Does the fact that Amelia’s indifference curve intersects with the custard axis violate any of the 5properties of indifference curves? Briefly support your answer.e. Give another utility function that represents…
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